Using molecular dynamics simulations, an embedded-atom model potential, and the mechanistic route, we have computed the pressure tensor and the surface tension γ of Ag-Au liquid alloys. Although the model generally underestimates γ for pure metals, calculations for a bulk planar slab exhibit nonlinear variations of γ with increasing gold concentration, which agree with experiments and can be accounted for by a perfect solution model. Calculations for various nanoscale droplets containing between 100 and 3200 atoms show a systematic decrease of γ with increasing droplet radius R. The positive Tolman length of the alloy determined from these size variations is estimated to vary slightly with gold concentration. The effects of temperature in the range 1300-1700 K are discussed.